C₁₁×#10667 #14587860

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10667

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#399
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

354 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,17,15,18,19,16)(20,21,24,29,26,30,25,39)(22,31,33,42,34,47,35,27)(23,28,37,44,38,46,40,45)(32,43,36,41,49,48,50,51);(12,13)(14,16)(15,18)(17,19)(20,22,25,33,26,34,24,35)(21,27,39,31,30,42,29,47)(23,36,40,49,38,50,37,32)(28,43,45,41,46,48,44,51);(13,16)(14,19)(17,18)(20,23)(21,28)(22,32)(24,37)(25,40)(26,38)(27,41)(29,44)(30,46)(31,48)(33,36)(34,49)(35,50)(39,45)(42,51)(43,47)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3655);